Michelle Obama recounted another incident at a gala dinner when someone asked Obama, who was dressed in a tuxedo, to get him coffee.
She also recalled a visit to the shopping chain store Target when a woman asked her to get something off a shelf.
“Because she didn’t see me as the first lady, she saw me as someone who could help her. Those kinds of things happen in life. So it isn’t anything new,” she said.
Although the Obamas said the situation has improved, they added that much more still needs to be done.
“The small irritations or indignities that we experience are nothing compared to what a previous generation experienced,” President Obama said in the interview for the magazine that goes on sale at newsstands on Friday.
“It’s one thing for me to be mistaken for a waiter at a gala. It’s another for my son to be mistaken for a robber and to be handcuffed, or worse, if he happens to be walking down the street and is dressed the way teenagers dress.”
The interview coincided with national protests after a grand jury in the New York City borough of Staten Island decided not to charge a white police officer over the death of Eric Garner, an unarmed black man, who was killed in a chokehold in July.
There were also protests after a Missouri grand jury in late November declined to indict a white police officer in the shooting death in August of an unarmed black man, Michael Brown.